Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 83, Issue 1, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-021-01616-z
Keywords
Fluorescence recovery after photobleaching; FRAP; Recovery curve; Confocal; Fluorescence microscopy; Reaction-diffusion
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Funding
- School of Mathematical Sciences, University of Nottingham
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This article investigates a two species reaction-diffusion FRAP model through asymptotic analysis, deriving new FRAP recovery curve approximation formulae and predicting sufficient conditions for parameter estimation using Fisher information. The predictions are verified through extensive computational simulations, and methods for extracting maximum information from FRAP data in theoretically inestimable cases are proposed.
Fluorescence recovery after photobleaching (FRAP) is a common experimental method for investigating rates of molecular redistribution in biological systems. Many mathematical models of FRAP have been developed, the purpose of which is usually the estimation of certain biological parameters such as the diffusivity and chemical reaction rates of a protein, this being accomplished by fitting the model to experimental data. In this article, we consider a two species reaction-diffusion FRAP model. Using asymptotic analysis, we derive new FRAP recovery curve approximation formulae, and formally re-derive existing ones. On the basis of these formulae, invoking the concept of Fisher information, we predict, in terms of biological and experimental parameters, sufficient conditions to ensure that the values all model parameters can be estimated from data. We verify our predictions with extensive computational simulations. We also use computational methods to investigate cases in which some or all biological parameters are theoretically inestimable. In these cases, we propose methods which can be used to extract the maximum possible amount of information from the FRAP data.
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